Just a small tip for any BLMs struggling with Sophia Ex.
Use your Aetherial Step.

Black/White:
Make a macro and step directly to your partner.

Arena Tilt + Knockback moves:
Step to partner to cancel the sliding effect. As long as you haven't fallen off yet, the step will stop you from falling further.
Even if they fall off, this will save you as long as the step kicks in. Just remember to wave /goodbye to your partner as you watch him fall off.

.....Well if your partner is already dead, you're out of luck....